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And the way that we'll do this is starting with talking about the discovery of the electron and the nucleus here.
在这之后,我们就可以通过,经典力学来描述一个原子。
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And then the potential energy, the energy is stored here due to the coulombic force of attraction between the electron and the nucleus.
然后说势能,位能其实就是,由电子和原子核之间的库仑引力而形成的能量。
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It was a classical model, right, so we could say the electron is exactly this far away from the nucleus.
这是个经典模型，对吧，我们说电子离,原子核就是这么远。
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So the probability of having an electron at the nucleus in terms of probability per volume is very, very high.
在单位体积内发现,一个电子的概率非常非常大。
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So I will take into account it that there is some contribution of both the nucleus and the electron.
所以我将考虑,那是原子核与电子,共同作用的结果。
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Because what it tells is that we can figure out exactly what the radius of an electron and a nucleus are in a hydrogen atom.
我们可以,准确的算出,氢原子中,电子。
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So, what we're looking at here is the force when we have two charged particles, one positive one negative -- here, the nucleus and an electron.
我们现在研究的是,一正一负俩个带电粒子之间的,作用力-在这里。
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We're going to be looking at the solutions to the Schrodinger equation for a hydrogen atom, and specifically we'll be looking at the binding energy of the electron to the nucleus.
我们将研究下氢原子薛定谔方程的解,特别是电子和核子的结合能,我们将研究这部分。
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So, the size still for an s orbital is larger than for a d orbital, but what we say is that an s electron can actually penetrate closer to the nucleus.
轨道的尺寸比,ｐ轨道还是要大，但我们说的是ｓ轨道可以,穿透到更接近原子核的地方。
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What I just spent many lectures discussing is the fact that we can not know how far away an electron is from the nucleus, so we can't actually know the radius of a certain atom.
我花了这么多课时所讨论的正是我们,不可能知道电子离原子核有多远这一事实，因此我们不可能知道某个原子的半径。
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That is the electron in its lowest orbit, to the nucleus of atomic hydrogen.
那就是氢原子原子核外电子，最低轨道到情况。
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So what is actually going to matter is how closely that electron can penetrate to the nucleus, and what I mean by penetrate to the nucleus is is there probability density a decent amount that's very close to the nucleus.
所以实际上有关系的是,电子可以穿越至原子核有多近,我所指的穿越至原子核是,这里有一定数量的概率密度,可以距离原子核非常近。
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So again, what we're saying here is that it is most likely in the 3 s orbital that we would find the electron 11 and 1/2 times further away from the nucleus than we would in a around state hydrogen atom.
同样我们,这里说的是,氢原子３ｓ轨道中,最可能找到电子的地方,是基态的１１．５倍。
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Again, we have continuous electron density from one nucleus to the other.
再说一遍，原子核间有不间断的电子云,相接没有节点，没有空缺。
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And, it involves a single electron orbiting a positively charged nucleus.
包含了一个单独的电子轨道,一个带正电荷的核。
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But luckily for us, there's a classical equation of motion that will, in fact, describe how the electron and nucleus change position or change their radius as a function of time.
但幸运的是，有一个,经典方程描述了电子和核子,位置或者它们直接的距离是,如何随时间变化的。
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But what's important is not where that most probable radius is when we're talking about the z effective it feels, what's more important is how close the electron actually can get the nucleus.
但重要的不是,最可能半径,当我们谈论它感到的有效电荷量的时候，更重要的是,电子实际上。
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So if you have some charge in the nucleus, but you also have repulsion with another electron, the net attractive charge that a given electron going to feel is actually less than that total charge in the nucleus.
所以如果在原子核中，有一些电荷但是你也有来自，另一个电子的排斥力,那么一个给定电子的,吸引电荷感觉到的事实上,小于原子核中的总电荷。
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I said what hold the bonds together, what holds two atoms together is the attractive force we have between each electron and the other nucleus.
我说过什么将它们结合在一起，将两个原子结合在一起的是一个吸引力,其中一个原子中的电子与另一个原子中的原子核之间。
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Because we know as we go to infinity, even though the density gets smaller and smaller and smaller, we still have electron density very far away from the nucleus.
因为我们知道即使到了无穷远处，尽管电子密度会变得非常非常非常小，但我们仍然有一定的电子密度，无论离原子核多远。
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Again we have the charge of the nucleus on plus 2, +2 but let's say this time the electron now is going to be very, very close to the nucleus.
对于我们的氦原子，我们有一次得到了原子核电荷量为,但是我们说这次电子。
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So, essentially we're just breaking it up into two parts that can be separated, and the part that is only dealing with the radius, so it's only a function of the radius of the electron from the nucleus.
所以本质上我们把它写成,两个可分离的部分，这部分，只与半径有关，它仅仅是，电子,到核子距离的函数。
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And, as I mentioned, we left off and as we started back here to describe the atom and how the atom holds together the nucleus and the electron using classical mechanics.
我之前提及过，我们上次,讲到应用经典力学如何描述,一个原子以及原子如何把质子,和电子束缚在一起，今天我们要。
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And if we go ahead and square that, then what we get is a probability density, and specifically it's the probability of finding an electron in a certain small defined volume away from the nucleus.
我们得到的是，一个概率密度，它是，在核子周围，某个很小的,特定区域,找到电子的概率,所以它是概率密度。
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So if we take this term, which is a volume term, and multiply it by probability over volume, what we're going to end up with is an actual probability of finding our electron at that distance, r, from the nucleus.
如果我们取这项，也就是体积项然后，乘以概率除以体积，我们能得到的就是真正在距离,原子核ｒ处找到电子的概率。
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So, basically what we're saying is if we take any shell that's at some distance away from the nucleus, we can think about what the probability is of finding an electron at that radius, and that's the definition we gave to the radial probability distribution.
本质上我们说的就是,如果我们在距离原子核,某处取一个壳层，我们可以考虑在这个半径处,发现电子的概率，这就是我们给出的,径向概率密度的定义。
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What I want to point out also is that this h hat, the Hamiltonian operator written out for the simplest case we can even imagine, which is a hydrogen atom where we only have one electron that we're dealing with, and of course, one nucleus.
我也想指出的是，我们能想到的最简单情况,的哈密顿算符，是一个只有一个电子,也只有一个原子核的氢原子。
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So when we talk about the size of multi-electron orbitals, they're actually going to be smaller because they're being pulled in closer to the nucleus because of that stronger attraction because of the higher charge of the nucleus in a multi-electron atom compared to a hydrogen atom.
所以当我们讨论,多电子轨道的尺寸，它们实际上会变得更小,因为多电子原子的原子核,相比于氢原子,有更高的电荷量所以,有更强的吸引力,所以可以拉的更近。
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We have a helium nucleus and one electron.
我们有一个氦核和一个电子。
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And when we do that we can see this curve, this probability curve, where we have a maximum probability of finding the electron this far away from the nucleus.
当我们这样做时，我们可以看到这个曲线，这个概率分布曲线，这里有发现,电子的最大概率。
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